Question

An open box is constructed by cutting out x-inch by x-inch squares from each of the four corners and folding up the sides. The original piece of cardboard has a length of 18 inches and a width of 24 inches. What is the volume of the box?
A)
(24−2⁢𝑥)⁢(18−2⁢𝑥)


B)
𝑥⁢(24−𝑥)⁢(18−𝑥)


C)
𝑥⁢(24−2⁢𝑥)⁢(18−2⁢𝑥)


D)
432 −4⁢𝑥2


E)
432⁢𝑥

Answer 1

Cutting out x-by-x squares and folding up gives height x and base dimensions 18−2x and 24−2x. So the volume is
V = x(18−2x)(24−2x),
which is choice C.